The present embodiments relate to positron emission tomography (PET).
PET systems and corresponding detectors have a limited field of view. Typically, the entire patient cannot be scanned with the patient in one position. In a step and shoot (S&S) approach to scan a greater portion of the patient, the patient is moved between sequential scans, but remains stationary for each of the scans. However, the gaps between blocks of detectors cause a drop in axial sensitivity when assembling the different scans for segment zero (2D) acquisitions. For three-dimensional (3D) acquisition, greater axial uniformity may be provided for S&S. Low sensitivity spots of various segments are mixed in image space, and therefore the loss of sensitivity only occurs in the end planes.
Continuous bed motion (CBM) acquisition performs a scan of the patient while the patient is moving through the PET system. CBM may improve the axial uniformity of PET images over S&S for 2D acquisitions. For 3D acquisitions, CBM acquisition may result in super-resolution images by oversampling the image in the axial direction. However, this advantage may not be applicable in the case of patient scanners, where effective resolution is relatively low due to high level noise using short clinical scans. One particular source of noise is noise in randoms or delayed coincidence. Both S&S and CBM acquisition reconstruction use a mean value of randoms events.
The expected randoms rate is used in Poisson model iterative image reconstruction. The expected randoms contribution to line-of-response (LOR) data may be estimated from the crystal singles rate, according to the randoms rate equation: rij=2τsisj,  (1)where indexes i and j denote crystals in coincidence, si is the mean single rate for a given crystal i, and 2τ is the coincidence time window.
The random count may be measured on the crystal level from the singles rates. However, some systems may acquire randoms (delay) projection data separately and not measure the crystal singles rate. The direct use of these noisy randoms measurements in the image reconstruction may lead to artifacts and increased image noise levels. The variance reduction of measured delayed coincidence sinograms may be performed through singles rate estimations from these data, followed by the construction of a mean random sinogram.
However, CBM acquisition significantly complicates this variance reduction. CBM causes summation over all detector pairs ij in the axial direction so that a per crystal singles rate cannot be determined. Further, the singles rate s is not constant and is a function of time due to the various activity parts of the patient as the patient passes through the field of view of the scanner. The result is an increase in the number of unknowns, complicating direct estimation of singles as function of time.